A158299 - OEIS

%I #29 Jul 15 2019 14:28:00

%S 1,5,5,7,13,25,25,85,91,65,61,35,85,125,65,341,145,455,181,91,125,305,

%T 265,425,217,425,205,175,421,325,481,455,305,725,325,637,685,905,425,

%U 1105,841,625,925,427,1183,1325,1105,341,817,1085,725,595,1405,1025

%N Numerators of averages of squares of the divisors of n.

%C Because Mathematica represents rational numbers with the smallest possible denominator, the terms of the sequence are numerators appropriate to such denominators.  For example, the divisors of 3 are 1 and 3, so their squares are 1 and 9.  The mean of those squares could be represented as 10/2 or 5/1.  Mathematica selects the latter so a(3) is 5 rather than 10. [From Harvey P. Dale, Oct 13 2011]

%C If m and n are coprime, f(m*n) divides f(m)*f(n). - _Robert Israel_, Jul 15 2019

%H Amiram Eldar, <a href="/A158299/b158299.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)

%p f:= proc(n) local D;

%p   D:= map(t -> t^2,numtheory:-divisors(n));

%p   numer(convert(D,`+`)/nops(D));

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Jul 15 2019

%t Numerator[Mean/@(Divisors[Range[60]]^2)] (* _Harvey P. Dale_, Oct 13 2011 *)

%t Array[Numerator[DivisorSigma[2, #]/DivisorSigma[0, #]] &, 100]; (* _Amiram Eldar_, Jul 15 2019 *)

%Y Cf. A001157, A000005, A158298 (for denominators).

%K nonn,frac

%O 1,2

%A _Jaroslav Krizek_, Mar 15 2009

%E Corrected and extended by Harvey P. Dale, Oct 13 2011